9,677 research outputs found

    Comparison of 13CO Line and Far-Infrared Continuum Emission as a Diagnostic of Dust and Molecular Gas Physical Conditions: I. Motivation and Modeling

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    Determining temperatures in molecular clouds from ratios of CO rotational lines or from ratios of continuum emission in different wavelength bands suffers from reduced temperature sensitivity in the high-temperature limit. In theory, the ratio of far-IR, submillimeter, or millimeter continuum to that of a 13CO (or C18O) rotational line can place reliable upper limits on the temperature of the dust and molecular gas. Consequently, far-infrared continuum data from the {\it COBE}/{\it DIRBE} instrument and Nagoya 4-m \cOone spectral line data were used to plot 240\um/13CO J=1-0 intensity ratios against 140\um/240\um dust color temperatures, allowing us to constrain the multiparsec-scale physical conditions in the Orion A and B molecular clouds. The best-fitting models to the Orion clouds consist of two components: a component near the surface of the clouds that is heated primarily by a very large-scale (i.e. ∼1\sim 1 kpc) interstellar radiation field and a component deeper within the clouds. The former has a fixed temperature and the latter has a range of temperatures that varies from one sightline to another. The models require a dust-gas temperature difference of 0±2\pm 2 K and suggest that 40-50% of the Orion clouds are in the form of dust and gas with temperatures between 3 and 10 K. These results have a number implications that are discussed in detail in later papers. These include stronger dust-gas thermal coupling and higher Galactic-scale molecular gas temperatures than are usually accepted, an improved explanation for the N(H2_2)/I(CO) conversion factor, and ruling out one dust grain alignment mechanism.Comment: The second version includes some discussion of why previous models of dust-gas thermal coupling were simplistic. Paper III in the series discusses this in more detail. Also, some minor errors were corrected. These errors in no way affect the final conclusion

    Comparison of 13CO Line and Far-Infrared Continuum Emission as a Diagnostic of Dust and Molecular Gas Physical Conditions: II. The Simulations: Testing the Method

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    The reliability of modeling the far-IR continuum to 13CO J=1-0 spectral line ratios applied to the Orion clouds (Wall 2006) is tested by applying the models to simulated data. The two-component models are found to give the dust-gas temperature difference, \DT, to within 1 or 2 K. However, other parameters like the column density per velocity interval and the gas density can be wrong by an order of magnitude or more. In particular, the density can be systematically underestimated by an order of magnitude or more. The overall mass of the clouds is estimated correctly to within a few percent. The one-component models estimate the column density per velocity interval and density within factors of 2 or 3, but their estimates of \DT can be wrong by 20 K. They also underestimate the mass of the clouds by 40-50%. These results may permit us to reliably constrain estimates of the Orion clouds' physical parameters, based on the real observations of the far-IR continuum and 13CO J=1-0 spectral line. Nevertheless, other systematics must be treated first. These include the effects of background/foreground subtraction, effects of the HI component of the ISM, and others. These will be discussed in a future paper (Wall 2006a).Comment: The somewhat severe restriction imposed by arXiv.org on file size required me to simplify some figures. Consequently, many figures show no error bar

    Identification Theory for Time Varying Models

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    The identification of time-varying coefficient regression models is investigated using an analysis of the classical information matrix. The variable coefficients are characterized by autoregressive stochastic processes, allowing the entire model to be case in state space form. Thus the unknown stochastic specification parameters and priors can be interpreted in terms of the coefficient matrices and initial state vector. Concentration of the likelihood function on these quantities allows the identification of each to be considered separately. Suitable restriction of the form of the state space model, coupled with the concept of controllability, lead to sufficient conditions for the identification of the coefficient transition parameters. Partial identification of the variance-covariance matrix for the random disturbances on the coefficients is established in a like manner. Introducing the additional concept of observability then provides for necessary and sufficient conditions for identification of the unknown priors. The results so obtained are completely analogous to those already established in the econometric literature, namely, that the coefficients of the reduced form are always identified subject to the absence of multicollinearity. Some consistency results are also presented which derive from the above approach.

    On the Identification of Time Varying Structures

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    The identifiability of reduced form econometric models with variable coefficients is investigated using the control theoretic concepts of uniform complete observability and uniform complete controllability. First, a variant of the state space representation of the traditional reduced form is introduced which transcribes the underlying non-stationary estimation problem into one particularly suited to a Kalman filtering solution. Using such a formulation, observability and controllability can be called upon to obtain a necessary and sufficient condition for identification of the specific parameterization. The results so obtained are completely analogous to those already established in the econometric literature, namely, that the parameters of the reduced form are always identified subject to the absence of multicollinearity(referred to as "persistent excitation" in the control literature). How-ever, now the multicollinearity condition is seen to depend on the structure of the parameter variations as well as the statistical nature of the explanatory variables. The verification of identifiability thus reduces to a check for uniform complete observability which can always be affected in econometric applications. Some consistency results are also presented which derive from the above approach.

    A Note on Optimal Smoothing for Time Varying Coefficient Problems

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    An algorithm is presented which provides a complete solution to the optimal estimation problem for time-varying parameters when no proper prior distribution is specified. The key ideas involve a combination of the information-form Kalman filter with the two-filter interpretation of the optimal smoother. The algorithm produces efficient estimates of the parameter trajectories over the entire sample, arid is equally applicable when a proper prior distribution has been specified.

    Common problems - and progress towards solutions - in the process mineralogy of rare earths

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    This is the author accepted manuscript. The final version is available from the publisher via the link in this recordThe geochemistry and mineralogy of rare earth element (REE) deposits is diverse and ranges from carbonatite-related deposits and alkaline rocks to mineral sands, ion adsorption clays, marine crusts, nodules and clays, by-products of phosphate and bauxite, and re-use of waste materials. Despite the large number of recent exploration projects, very little additional REE production has started. An in-depth understanding of the mineralogy is essential for process design and all of the deposit types have mineralogical advantages and challenges, which will be reviewed and explained. For example, the deposits with the best established processing routes are monazite-bearing mineral sands but monazite radioactivity renders most unusable. Ion adsorption clays are easily leachable but deposits are low grade and shallow so new environmentally-friendly leaching techniques are needed. The diverse mineralogy of alkaline rocks has required development of processing routes for rare minerals such as steenstrupine and eudialyte. Carbonatites tend to have high proportions of the least valuable, lightest REE in REE fluorcarbonates or monazite. A deposit with two ore minerals, REE fluorcarbonate and apatite, that combine to give a REE profile close to that required by industry has an advantage if the ore minerals can be recovered efficiently

    Asymptotic Charges Cannot Be Measured in Finite Time

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    To study quantum gravity in asymptotically flat spacetimes, one would like to understand the algebra of observables at null infinity. Here we show that the Bondi mass cannot be observed in finite retarded time, and so is not contained in the algebra on any finite portion of I+{\mathscr{I}}^+. This follows immediately from recently discovered asymptotic entropy bounds. We verify this explicitly, and we find that attempts to measure a conserved charge at arbitrarily large radius in fixed retarded time are thwarted by quantum fluctuations. We comment on the implications of our results to flat space holography and the BMS charges at I+{\mathscr{I}}^+.Comment: 9 pages, 3 figures. v2 typos fixed and minor addition
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